Abstract and Applied Analysis

Infinitely Many Elliptic Solutions to a Simple Equation and Applications

Long Wei and Yang Wang

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Abstract

Based on auxiliary equation method and Bäcklund transformations, we present an idea to find infinitely many Weierstrass and Jacobi elliptic function solutions to some nonlinear problems. First, we give some nonlinear iterated formulae of solutions and some elliptic function solutions to a simple auxiliary equation, which results in infinitely many Weierstrass and Jacobi elliptic function solutions of the simple equation. Then applying auxiliary equation method to some nonlinear problems and combining the results with exact solutions of the auxiliary equation, we obtain infinitely many elliptic function solutions to the corresponding nonlinear problems. The employed approach is powerful and can be also applied to solve other nonlinear differential equations.

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 582532, 9 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393511994

Digital Object Identifier
doi:10.1155/2013/582532

Mathematical Reviews number (MathSciNet)
MR3090268

Zentralblatt MATH identifier
1302.35113

Citation

Wei, Long; Wang, Yang. Infinitely Many Elliptic Solutions to a Simple Equation and Applications. Abstr. Appl. Anal. 2013 (2013), Article ID 582532, 9 pages. doi:10.1155/2013/582532. https://projecteuclid.org/euclid.aaa/1393511994


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